Avogadro's Law states that, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas. In simpler terms, equal volumes of different gases contain the same number of molecules when they are at the same temperature and pressure. 

Since both Oxygen and Nitrogen contain the same volume of gases at the same temperature and pressure, their number of moles will also be the same. i.e If Nitrogen contains 5.0 moles, then Oxygen will also contain 5.0moles.

Thus, number of moles of oxygen, n = 5.0 moles

Molar mass of O\(_2\) = 16 x 2 = 32g/mol

But  n = \(\frac{m}{M}\) 

 m = n x M = 5 X 32 = 160.0g